Consider the following equation.
\[
7 y-3=-3(4-x)
\]
Step 2 of 2 : Find the equation of the line which passes through the point (6, - 2) and is parallel to the given line. Express your answer in slope-intercept form. Simplify your answer:

Step 1 ：Consider the following equation: \(7y - 3 = -3(4 - x)\).

Step 2 ：First, we need to rearrange the equation to the form \(y = mx + c\), where \(m\) is the slope of the line.

Step 3 ：Doing so, we get \(y = \frac{3}{7}x - \frac{9}{7}\).

Step 4 ：From this, we can see that the slope of the line is \(\frac{3}{7}\).

Step 5 ：We are asked to find the equation of the line which passes through the point (6, -2) and is parallel to the given line.

Step 6 ：Since parallel lines have the same slope, the slope of the new line will also be \(\frac{3}{7}\).

Step 7 ：We can use the point-slope form of the line equation, \(y - y1 = m(x - x1)\), where \((x1, y1)\) is the point through which the line passes, to find the equation of the line.

Step 8 ：Substituting the given point (6, -2) and the slope \(\frac{3}{7}\) into the equation, we get \(y = \frac{3}{7}x - \frac{32}{7}\).

Step 9 ：Final Answer: The equation of the line which passes through the point (6, - 2) and is parallel to the given line is \(\boxed{y = \frac{3}{7}x - \frac{32}{7}}\).